Abstract

Measurements of the dispersion of the refractive index using a nonlinear interferometer are described. A sample of the optical material to be measured is interposed between two optically nonlinear crystals, and a moderately intense laser is passed through the combination. By observing the interference between the second harmonics produced in the two nonlinear crystals, the difference between the refractive indices of the sample at the laser frequency and its second harmonic frequency can be determined very precisely. We have used the interferometer to measure the dispersion in several gases between 1064 and 532 nm. We have also used it to determine the dispersion of two transparent solids. The method can measure the index difference to better than 0.1%, which for gases such as helium represents an absolute accuracy of ∼10−9.

© 1986 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), Chap. 23.
  2. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 148.
  3. D. Eimerl, “The Potential for Efficient Frequency Conversion at High Average Powers, Using Solid State Nonlinear Optical Materials,” LLNL ReportUCRL 20565.
  4. F. A. Hopf, A. Tomita, G. Al-Jumaily, “Second Harmonic Interferometers,” Opt. Lett. 5, 386 (1980).
    [CrossRef] [PubMed]
  5. F. A. Hopf, A. Tomita, G. Al-Jumaily, M. Cervantes, T. Liepmann, “Second Harmonic Interferometers II,” Opt. Commun. 36, 487 (1981).
    [CrossRef]
  6. F. A. Hopf, M. Cervantes, “Nonlinear Optical Interferometer,” Appl. Opt. 21, 668 (1982).
    [CrossRef] [PubMed]
  7. T. W. Liepmann, F. A. Hopf, “Common Path Interferometer based on Second Harmonic Generation,” Appl. Opt. 24, 1485 (1985).
    [CrossRef] [PubMed]
  8. E. Sinofsky, F. Hopf, “Interferometrically Measuring Phase Mismatch for Second Harmonic Generation,” Appl. Opt. 24, 2206 (1985).
    [CrossRef] [PubMed]
  9. F. Zernike, J. E. Midwinter, Applied Nonlinear Optics (Wiley-Interscience, New York, 1973).
  10. D. Eimerl, Lawrence Livermore National Laboratory Annual Report (1980), UCRL 50021-80, p. 2-255.
  11. R. W. Ditchburn, Light (Wiley-Interscience, New York, 1963), Chap. 9.
  12. P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effect of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8, 21 (1962).
    [CrossRef]
  13. W. Driscoll, Ed. Handbook of Optics (McGraw-Hill, New York, 1978), Chap. 7.

1985 (2)

1982 (1)

1981 (1)

F. A. Hopf, A. Tomita, G. Al-Jumaily, M. Cervantes, T. Liepmann, “Second Harmonic Interferometers II,” Opt. Commun. 36, 487 (1981).
[CrossRef]

1980 (1)

1962 (1)

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effect of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Al-Jumaily, G.

F. A. Hopf, A. Tomita, G. Al-Jumaily, M. Cervantes, T. Liepmann, “Second Harmonic Interferometers II,” Opt. Commun. 36, 487 (1981).
[CrossRef]

F. A. Hopf, A. Tomita, G. Al-Jumaily, “Second Harmonic Interferometers,” Opt. Lett. 5, 386 (1980).
[CrossRef] [PubMed]

Cervantes, M.

F. A. Hopf, M. Cervantes, “Nonlinear Optical Interferometer,” Appl. Opt. 21, 668 (1982).
[CrossRef] [PubMed]

F. A. Hopf, A. Tomita, G. Al-Jumaily, M. Cervantes, T. Liepmann, “Second Harmonic Interferometers II,” Opt. Commun. 36, 487 (1981).
[CrossRef]

Ditchburn, R. W.

R. W. Ditchburn, Light (Wiley-Interscience, New York, 1963), Chap. 9.

Eimerl, D.

D. Eimerl, “The Potential for Efficient Frequency Conversion at High Average Powers, Using Solid State Nonlinear Optical Materials,” LLNL ReportUCRL 20565.

D. Eimerl, Lawrence Livermore National Laboratory Annual Report (1980), UCRL 50021-80, p. 2-255.

Hopf, F.

Hopf, F. A.

Jenkins, F.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), Chap. 23.

Liepmann, T.

F. A. Hopf, A. Tomita, G. Al-Jumaily, M. Cervantes, T. Liepmann, “Second Harmonic Interferometers II,” Opt. Commun. 36, 487 (1981).
[CrossRef]

Liepmann, T. W.

Maker, P. D.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effect of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Midwinter, J. E.

F. Zernike, J. E. Midwinter, Applied Nonlinear Optics (Wiley-Interscience, New York, 1973).

Nisenoff, M.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effect of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Savage, C. M.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effect of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Sinofsky, E.

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 148.

Terhune, R. W.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effect of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Tomita, A.

F. A. Hopf, A. Tomita, G. Al-Jumaily, M. Cervantes, T. Liepmann, “Second Harmonic Interferometers II,” Opt. Commun. 36, 487 (1981).
[CrossRef]

F. A. Hopf, A. Tomita, G. Al-Jumaily, “Second Harmonic Interferometers,” Opt. Lett. 5, 386 (1980).
[CrossRef] [PubMed]

White, H.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), Chap. 23.

Zernike, F.

F. Zernike, J. E. Midwinter, Applied Nonlinear Optics (Wiley-Interscience, New York, 1973).

Appl. Opt. (3)

Opt. Commun. (1)

F. A. Hopf, A. Tomita, G. Al-Jumaily, M. Cervantes, T. Liepmann, “Second Harmonic Interferometers II,” Opt. Commun. 36, 487 (1981).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effect of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Other (7)

W. Driscoll, Ed. Handbook of Optics (McGraw-Hill, New York, 1978), Chap. 7.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), Chap. 23.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 148.

D. Eimerl, “The Potential for Efficient Frequency Conversion at High Average Powers, Using Solid State Nonlinear Optical Materials,” LLNL ReportUCRL 20565.

F. Zernike, J. E. Midwinter, Applied Nonlinear Optics (Wiley-Interscience, New York, 1973).

D. Eimerl, Lawrence Livermore National Laboratory Annual Report (1980), UCRL 50021-80, p. 2-255.

R. W. Ditchburn, Light (Wiley-Interscience, New York, 1963), Chap. 9.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the nonlinear interferometer. Crystals 1 and 2 are second harmonic generators with lengths l1 and l2 separated by a distance l. The second harmonic field E2 generated in crystal 1 interferes with field E 2 generated in crystal 2 at the detector (not shown).

Fig. 2
Fig. 2

Details of the apparatus used in this work. PD1, 2, and 3 are vacuum photodiodes. RG1000, B618, and K65 are filters. PH is an iris diaphragm. Not shown are the BOXCAR integrators and computer used for data aquisition. For the Maker-fringe experiments, the cell is replaced by a plate which can be rotated about an axis perpendicular to the laser beam.

Fig. 3
Fig. 3

Second harmonic intensity as a function of pressure for helium in the 112.48-cm cell. The solid line is the best fit to Eq. (11).

Fig. 4
Fig. 4

Second harmonic intensity as a function of pressure for nitrogen in the 10.41-cm cell with the best fit curve as in Fig. 3. The noise levels shown here are typical and largely due to laser pointing instability.

Fig. 5
Fig. 5

Dispersion in air as a point on the mixing line for nitrogen and oxygen. The proportions assumed were N2:79% and O2:21%. The pressure of small amounts of argon and carbon dioxide were ignored.

Fig. 6
Fig. 6

Maker fringes for a plate of lithium fluoride. The solid line is the best fit to Eqs. (10) and (17) and corresponds to Δn = 0.0069. The discrepancy between data and fit near θ = 0 may be due to neglect of reflection losses.

Fig. 7
Fig. 7

Maker fringes for a glass plate. The least-squares fit gives Δn = 0.0133.

Tables (2)

Tables Icon

Table I Coherence Lengths of Gasesa

Tables Icon

Table II Dispersion of Gasesa

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

n 2 = a + b / ( 1 λ 0 2 / λ 2 ) .
ν = n D 1 n F n C .
Δ n = n ( 2 ω ) n ( ω ) .
E = E 2 + E 2 .
ϕ = Δ n 4 π l λ + ϕ 0 ,
Δ n = Δ n 0 ρ .
l c = λ 2 Δ n 0 ,
E = E 0 [ exp ( i Δ k 1 l 1 ) 1 i Δ k 1 + R · exp ( i Δ k 1 l 1 ) · exp ( i Δ k 2 l 2 ) 1 i Δ k 2 ] ,
R = T · ( l 2 / l 1 ) · exp ( i ϕ )
I = I 2 + I 2 + 2 ( I 2 · I 2 ) ½ cos ϕ
I ( P ) = a + b cos ( d + cPl ) .
c = 4 π Δ n 0 λ P 0 ( T 0 / T ) .
n T X A n A + X B n B .
X A , B = P A , B P A + P B P A , B P T .
Δ n T = Δ n s P T + ½ ( Δ n B Δ n s ) P B ,
Δ n T = ( X s Δ n s + X B Δ n B ) P T .
L = L 0 cos Θ int .
cos Θ int = ( 1 sin 2 Θ ext n ) ½ .
C ( m rad p sia - cm )

Metrics